Approximation using √2 ≈ 1.4142: Find the approximate value of √(2/9).

Introduction / Context:We are asked to estimate a simple radical with a known approximation for √2. Recognizing the algebraic manipulation helps compute quickly without a calculator.

Given Data / Assumptions:√2 ≈ 1.4142. We need √(2/9).

Concept / Approach:Use √(a/b) = √a / √b. Hence √(2/9) = √2 / 3. Substitute the given approximation √2 ≈ 1.4142 and divide by 3.

Step-by-Step Solution:

Verification / Alternative check:Square 0.4714: approximately 0.2222, which is close to 2/9 ≈ 0.2222.

Why Other Options Are Wrong:0.2321, 0.3174, 0.4174, and 0.5770 correspond to other unrelated radicals or inverses.

Common Pitfalls:Confusing √(2/9) with 1/√(2/9) = 3/√2 (which would be about 2.121), not asked here.

Final Answer:0.4714